75.12.29 problem 303

Internal problem ID [16824]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 12. Miscellaneous problems. Exercises page 93
Problem number : 303
Date solved : Monday, March 31, 2025 at 03:23:14 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (3 x +3 y+a^{2}\right ) y^{\prime }&=4 x +4 y+b^{2} \end{align*}

✓ Maple. Time used: 0.044 (sec). Leaf size: 79

ode:=(3*x+3*y(x)+a^2)*diff(y(x),x) = 4*x+4*y(x)+b^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (4 a^{2}-3 b^{2}\right ) \operatorname {LambertW}\left (\frac {3 \,{\mathrm e}^{\frac {3 a^{2}+3 b^{2}-49 c_1 +49 x}{4 a^{2}-3 b^{2}}}}{4 a^{2}-3 b^{2}}\right )}{21}-\frac {a^{2}}{7}-\frac {b^{2}}{7}-x \]

✓ Mathematica. Time used: 60.053 (sec). Leaf size: 97

ode=(3*(x+y[x])+a^2)*D[y[x],x]==4*(x+y[x])+b^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{21} \left (-3 \left (a^2+b^2+7 x\right )+\left (4 a^2-3 b^2\right ) W\left (-4 \left (2^{\frac {3 b^2}{2 a^2}-2} e^{\frac {49 x-3 b^2 (-1+c_1)}{4 a^2}-1+c_1}\right ){}^{\frac {4 a^2}{4 a^2-3 b^2}}\right )\right ) \]

✓ Sympy. Time used: 1.949 (sec). Leaf size: 68

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
y = Function("y") 
ode = Eq(-b**2 - 4*x + (a**2 + 3*x + 3*y(x))*Derivative(y(x), x) - 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {a^{2}}{7} - \frac {b^{2}}{7} - x + \frac {\left (4 a^{2} - 3 b^{2}\right ) W\left (- \frac {3 e^{\frac {C_{1} + 3 a^{2} + 3 b^{2} + 49 x}{4 a^{2} - 3 b^{2}}}}{4 a^{2} - 3 b^{2}}\right )}{21} \]